Simplify the following expression: $ a = \dfrac{9}{5x - 9} + \dfrac{-5}{7} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{9}{5x - 9} \times \dfrac{7}{7} = \dfrac{63}{35x - 63} $ Multiply the second expression by $\dfrac{5x - 9}{5x - 9}$ $ \dfrac{-5}{7} \times \dfrac{5x - 9}{5x - 9} = \dfrac{-25x + 45}{35x - 63} $ Therefore $ a = \dfrac{63}{35x - 63} + \dfrac{-25x + 45}{35x - 63} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{63 - 25x + 45}{35x - 63} $ $a = \dfrac{-25x + 108}{35x - 63}$